<title>Differentiator (inverting)</title>
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<p>
This circuit calculates the derivative of the input, meaning that the
output voltage is proportional to the (negative) rate of change of the input voltage.
<p>
The voltage across the capacitor is proportional
to the charge stored in it (the integral of the current).  The <a
href="http://en.wikipedia.org/wiki/Operational_amplifier">op-amp</a>
attempts to keep its &ndash; input at the same voltage as the + input
(which is at ground), so the voltage drop across the capacitor must always
be equal to the input voltage.  This requires the op-amp to have a negative
voltage when the input voltage is rising (to drain the capacitor to compensate),
and a positive voltage when the input voltage is falling.  If the
input voltage changes too fast, the op-amp will hit its upper or lower
limit and so it won't be able to keep the &ndash; input at ground all
the time.

<p>
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